M ar 2 02 0 N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions (original) (raw)
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Journal of High Energy Physics
In this work we present the ultra-relativistic N-extended AdS Chern-Simons supergravity theories in three spacetime dimensions invariant under N-extended AdS Carroll superalgebras. We first consider the (2, 0) and (1, 1) cases; subsequently, we generalize our analysis to N = (N , 0), with N even, and to N = (p, q), with p, q > 0. The N-extended AdS Carroll superalgebras are obtained through the Carrollian (i.e., ultra-relativistic) contraction applied to an so(2) extension of osp(2|2) ⊗ sp(2), to osp(2|1) ⊗ osp(2, 1), to an so(N) extension of osp(2|N) ⊗ sp(2), and to the direct sum of an so(p) ⊕ so(q) algebra and osp(2|p) ⊗ osp(2, q), respectively. We also analyze the flat limit (→ ∞, being the length parameter) of the aforementioned N-extended Chern-Simons AdS Carroll supergravities, in which we recover the ultra-relativistic N-extended (flat) Chern-Simons supergravity theories invariant under N-extended super-Carroll algebras. The flat limit is applied at the level of the superalgebras, Chern-Simons actions, supersymmetry transformation laws, and field equations.
Extended supergravity: Chern–Simons theories in 2+1 dimensions
Journal of Mathematical Physics, 1991
In this paper de Sitter supergravity theories in 2+1 dimensions with positive cosmological constant as Chern–Simons gauge theories of the algebra OSp(M‖2;C) are constructed. Starting from anti-de Sitter supergravity theories based on OSp(M‖2;R)×OSp(M‖2;R) algebras, a particular Inonu–Wigner contraction is used to construct a large class of super Poincaré supergravity theories with nontrivial internal symmetries. Other models based on algebras SL(M‖N) and the exceptional super Lie algebras are also discussed. The classical consistency of our de Sitter supergravity theories is discussed.
(2+1)-dimensional supergravity invariant under the AdS-Lorentz superalgebra
arXiv: High Energy Physics - Theory, 2014
It is shown that the semi-simple extended Poincare superalgebra can be obtained from the orthosymplectic algebra OSp(N,4) (Anti-de-Sitter superalgebra) using the S-expansion procedure. The S-expansion mechanism is used to obtain the (i) Casimir operators for the semi-simple extended Poincare superalgebra and (ii) the corresponding invariant tensors which allows us the construction of a (2+1)-dimensional Lagrangian for Chern-Simons supergravity.
ℵ0-extended supergravity and Chern-Simons theories
Nuclear Physics B, 1996
We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in threedimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ 0 (Aleph-Null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ 0 supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond N = 4. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three-dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as N = 1 self-dual supersymmetric Yang-Mills theory or N = 1 supergravity theory that can generate ℵ 0 globally and locally supersymmetric theories in three-dimensions. As an interesting application, we present ℵ 0 supergravity Liouville theory in two-dimensions after appropriate dimensional reduction from threedimensions.
Three-dimensional Poincaré supergravity and N-extended supersymmetric BMS3 algebra
Physics Letters B
A new approach for obtaining the three-dimensional Chern-Simons supergravity for the Poincaré algebra is presented. The N-extended Poincaré supergravity is obtained by expanding the super Lorentz theory. We extend our procedure to their respective asymptotic symmetries and show that the N = (1, 2, 4) super-BMS 3 appear as expansions of one Virasoro superalgebra. Interestingly, the N-extended super-BMS 3 obtained here are not only centrally extended but also endowed with internal symmetry. We also show that the N-extended super Poincaré algebras with both central and automorphism generators are finite subalgebras.
Super-BMS_3 algebras from N=2 flat supergravities
2016
We consider two possible flat space limits of three dimensional N = (1,1) AdS supergravity. They differ by how the supercharges are scaled with the AdS radius ℓ: the first limit (democratic) leads to the usual super-Poincare theory, while a novel `twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non- and ultra-relativistic limits of the N=(1,1) Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.
Fundamental extended objects for Chern–Simons supergravity
Physics Letters B, 2000
We propose a class of models in which extended objects are introduced in Chern-Simons supergravity in such a way that those objects appear on the same footing as the target space. This is motivated by the idea that branes are already first quantized object, so that it is desirable to have a formalism that treats branes and their target space in a similar fashion. Accordingly, our models describe interacting branes, as gauge systems for supergroups. We also consider the case in which those objects have boundaries, and discuss possible links to superstring theory and/or M-theory, by studying the fermionic κ -symmetry of the action.
Higher dimensional Chern-Simons supergravity
Physical Review D, 1996
A Chern-Simons action for supergravity in odddimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincaré group. In 2 + 1 dimensions the gauge group reduces to super-Poincaré, while for D = 5 it is super-Poincaré with a central charge. In general, the extension is obtained by the addition of a 1-form field which transforms as an antisymmetric fifth-rank tensor under Lorentz rotations. Since the Lagrangian is a Chern-Simons density for the supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.
The quantum theory of Chern-Simons supergravity
Journal of High Energy Physics, 2019
We consider AdS 3 N-extended Chern-Simons supergravity (à la Achucarro-Townsend) and we study its gauge symmetries. We promote those gauge symmetries to a BRST symmetry and we perform its quantization by choosing suitable gauge-fixings. The resulting quantum theories have different features which we discuss in the present work. In particular, we show that a special choice of the gauge-fixing correctly reproduces the Ansatz by Alvarez, Valenzuela and Zanelli for the graphene fermion.
Super-BMS3 algebras from N = 2 mathcalN=2\mathcal{N}=2mathcalN=2 flat supergravities
Journal of High Energy Physics
We consider two possible flat space limits of three dimensional N = (1, 1) AdS supergravity. They differ by how the supercharges are scaled with the AdS radius ℓ: the first limit (democratic) leads to the usual super-Poincaré theory, while a novel 'twisted' theory of supergravity stems from the second (despotic) limit. We then propose boundary conditions such that the asymptotic symmetry algebras at null infinity correspond to supersymmetric extensions of the BMS algebras previously derived in connection to non-and ultra-relativistic limits of the N = (1, 1) Virasoro algebra in two dimensions. Finally, we study the supersymmetric energy bounds and find the explicit form of the asymptotic and global Killing spinors of supersymmetric solutions in both flat space supergravity theories.